Dividend Discount Model (DDM)

The dividend discount model (DDM) is a method of valuing a stock by treating its price as the present value of every dividend the company is expected to pay its shareholders in the future. The future dividends are discounted at the shareholders' required rate of return, often called the cost of equity. The model is used by equity analysts, by investors estimating the intrinsic value of mature dividend-paying companies such as utilities and banks, and by regulators when setting allowed returns for regulated firms.

The idea was set out by the American economist John Burr Williams in The Theory of Investment Value (1938). Its best-known form, the constant-growth or Gordon growth model, is associated with Myron J. Gordon, who developed it with Eli Shapiro in 1956 and in later work. The DDM is a special case of discounted cash-flow valuation and rests on the time value of money; the same logic gives the net present value of a project.

Picture an apple tree you might buy. You do not want the tree for its wood; you want the apples it will give you every year. A sensible price is the value today of all those future harvests, with later harvests counting for less because you have to wait for them and because the tree might get sick.

A share in a company that pays dividends works the same way. The dividends are the apples. The DDM adds up what all the future dividends are worth today, and that total is what the model says the share is worth. If the harvest is expected to grow a little every year, the tree is worth more.

If dividends are expected to grow at a constant rate forever, the infinite sum collapses to a simple formula:

• $P_0$ is the estimated value of the share today.
• $D_1$ is the dividend expected over the next year.
• $r$ is the required return on equity, written as a decimal.
• $g$ is the constant annual growth rate of dividends, which must be lower than $r$.

Worked example: a company is expected to pay a dividend of 2.00 next year, growing at 3% a year, and investors require 8%. The model gives $2.00 \div (0.08 - 0.03) = 40.00$. If the required return rises to 9%, the value falls to $2.00 \div 0.06 = 33.33$, a drop of about 17% from a one-point change. The formula can also be rearranged to $r = D_1 \div P_0 + g$: the expected return equals the dividend yield plus dividend growth.

When growth is zero the model becomes a perpetuity, $P_0 = D \div r$, which is how fixed-dividend preferred stock is often valued.

The required return $r$ is usually estimated with the Capital Asset Pricing Model (CAPM) as the risk-free rate plus a risk premium scaled by the stock's beta. Growth $g$ is often estimated as the share of earnings retained multiplied by the return on equity, or taken from analysts' forecasts of earnings per share.

• Two-stage and multi-stage models. These allow a period of fast growth, typical of a younger firm, before settling into a lower long-run rate. Each stage is discounted separately and a terminal value is added at the end.
• H-model. Assumes growth declines in a straight line from a high rate to a stable one, giving a shortcut for a fading growth period.
• Total-payout models. Because many companies return cash through share buybacks rather than dividends, some analysts discount total payouts or free cash flow to equity instead.

The model also links to the price-to-earnings ratio: dividing both sides of the Gordon formula by earnings shows that a higher payout, faster growth or a lower required return all justify a higher P/E.

The DDM is most at home with stable, mature businesses that pay a predictable share of profit as dividends, such as electricity and water utilities, telecom operators and large banks, often classed as blue-chip stocks. Utility regulators in the United States have long used DDM-based estimates to set the return a regulated company may earn on equity. Value investors use it as one cross-check on whether a share trades below its estimated worth, and strategists apply it to a whole stock market index to back out the implied equity risk premium.

• Non-payers. Many companies, particularly a young growth stock, pay no dividend, so the model cannot be applied directly.
• Sensitivity. Because value depends on the gap between $r$ and $g$, small errors in either produce large swings, and the model breaks down entirely if $g$ approaches $r$.
• Payout policy. Merton Miller and Franco Modigliani argued in 1961 that, under idealized conditions, how a firm splits profit between dividends and retained earnings does not change its value. In practice dividends can be cut, raised or replaced by buybacks, so they may track the business imperfectly.
• Forever is long. A constant growth rate assumed to last indefinitely must be no higher than long-run growth of the economy, yet analysts sometimes plug in rates that imply the company eventually outgrows the world.

• Aswath Damodaran, NYU Stern School of Business: valuation data and teaching materials